Jean-Sébastien Tancrez

Assessing the impact of stochasticity for operating theater sizing

Over the last few decades, rational health care management and, in particular, operating theater planning, has attracted increased attention from practitioners and from the scientific community. However, although the operating theater environment is clearly stochastic, the impact of this randomness has often been ignored. In practice, simple rules based largely on past experience (such as keeping a safety margin), are most frequently used when making plans for the operating theater. In this paper, we propose an approach to help rationalize, at a strategic decision-making level, the way in which stochasticity can be taken into account in operating theater management, to help in the sizing and in the allocation of capacity. The three main sources of randomness are considered: durations of operations, unexpected emergencies and blocking because of a full recovery unit. Based on the Markov theory, our tool enables several performance measures to be estimated. An operating theater manager can use our approach to make informed decisions and assess, for example, the disruption of the planning by emergencies, the waiting times for emergency patients, the impact of the recovery unit, or the distribution of the working time. In particular, our approach helps determine the number of operations that should be planned in order to keep expected overtime limited. The tool is described in detail, discussed, and applied to the illustrative case of a Belgian hospital.

How stochasticity and emergencies disrupt the surgical schedule

In health care system, the operating theatre is recognized as having an important role, notably in terms of generated income and cost. Its management, and in particular its scheduling, is thus a critical activity, and has been the sub ject of many studies. However, the stochasticity of the operating theatre environment is rarely considered while it has considerable effect on the actual working of a surgical unit. In practice, the planners keep a safety margin, let’s say 15% of the capacity, in order to absorb the effect of unpredictable events. However, this safety margin is most often chosen sub jectively, from experience. In this paper, our goal is to rationalize this process. We want to give insights to managers in order to deal with the stochasticity of their environment, at a tactical–strategic decision level. For this, we propose an analytical approach that takes account of the stochastic operating times as well as the disruptions caused by emergency arrivals. From our model, various performance measures can be computed: the emergency disruption rate, the waiting time for an emergency, the distribution of the working time, the probability of overtime, the average overtime, etc. In particular, our tool is able to tell how many operations can be scheduled per day in order to keep the overtime limited.

A heuristic algorithm for solving large location–inventory problems with demand uncertainty

In this paper, we analyze a location–inventory problem for the design of large supply chain networks with uncertain demand. We give a continuous non-linear formulation that integrates location, allocation and inventory decisions, and includes the costs of transportation, cycle inventory, safety stock, ordering and facility opening. Then, relying on the fact that the model becomes linear when certain variables are fixed, we propose a heuristic algorithm that solves the resulting linear program and uses the solution to improve the variable estimations for the next iteration. In order to show the efficiency of the algorithm, we compare our results with those of the conic quadratic formulation of the problem. Computational experiments show that the heuristic algorithm can be efficiently used to find fast and close to optimal solutions for large supply chain networks. Finally, we provide managerial insights regarding the ways in which demand uncertainty, risk pooling and safety stocks at retailers affect the design of a supply chain.

A Tight Bound on the Throughput of Queueing Networks with Blocking

In this paper, we present a bounding methodology that allows to compute a tight bound on the throughput of fork-join queueing networks with blocking and with general service time distributions. No exact models exist for queueing networks with general service time distributions and, consequently, bounds are the only certain information available. The methodology relies on two ideas. First, probability mass fitting (PMF) discretizes the service time distributions so that the evolution of the modified system can be modelled by a discrete Markov chain. Second, we show that the critical path can be computed with the discretized distributions and that the same sequence of jobs offers a bound on the original throughput. The tightness of the bound is shown on computational experiments (error on the order of one percent). Finally, we discuss the extension to split-and-merge networks and the approximate estimations of the throughput.

Étude de la perturbation par les urgences du planning opératoire

Etant à la fois centre de dépense et source de revenus, le quartier opératoire fait l’objet d’une attention particulière au sein de la gestion hospitalière. Dans cet article, nous étudions le caractère stochastique de cet environnement qui, bien que négligé dans la littérature, est important en pratique. Nous considérons la perturbation engendrée par les urgences, ainsi que les durées aléatoires des opérations planifiées ou urgentes. Notre modèle, basé sur la théorie markovienne, permet de mesurer l’impact des aléas sur le planning des opérations, afin notamment de réserver des plages destinées à l’absorption des aléas et d’évaluer l’opportunité de dédier des salles aux urgences.